Dispersion of biased swimming micro-organisms in a fluid flowing through a tube

Abstract

Classical Taylor-Aris dispersion theory is extended to describe the transport of suspensions of self-propelled dipolar cells in a tubular flow. General expressions for the mean drift and effective diffusivity are determined exactly in terms of axial moments and compared with an approximation a la Taylor. As in the Taylor-Aris case, the skewness of a finite distribution of biased swimming cells vanishes at long times. The general expressions can be applied to particular models of swimming micro-organisms, and thus be used to predict swimming drift and diffusion in tubular bioreactors, and to elucidate competing unbounded swimming drift and diffusion descriptions. Here, specific examples are presented for gyrotactic swimming algae.

Dispersion of swimming algae in laminar and turbulent channel flows: consequences for photobioreactors

“…However, as detailed above, recent studies show that the distribution and consequent dispersion of swimming cells in flows, including biotechnologically interesting species such as Dunaliella, should be very different from that of passive tracers [18,19]. For example, if cells disperse differently to nutrients in a reactor they will separate, which could have catastrophic consequences for growth.…”

“…In a recent study, Bees & Croze [18] extend the classical Taylor-Aris analysis of dispersion in a laminar flow in a tube to the case of biased swimming algae. The Bees & Croze dispersion theory provides a general theoretical framework to describe the dispersion of biased micro-swimmers in confined geometries, such as pipes and channels.…”

“…To make predictions for the dispersion of particular organisms, specific functional expressions for the swimming characteristics need to be obtained from microscopic models. For example, using expressions for the mean swimming orientation q and diffusivity D from the so-called Fokker-Planck (FP) model [12], Bees & Croze [18] found that gyrotaxis can significantly modify the axial dispersion of swimming algae (such as Chlamydomonas spp.) in a pipe flow relative to the case of passive tracers (or dissolved chemicals).…”

Dynamics of a homogeneous active dumbbell system

“…Some of these are: the existence of orientationally ordered states in two spatial dimensions [16,17], spatial phase separation into an aggregated phase and gas-like regions for sufficiently large packing fractions in the absence of attractive interactions [18][19][20][21][22][23][24][25][26][27], giant density fluctuations [19,22,28,29] and accumulation at boundaries [30][31][32], spontaneous collective motion [33], glassy features [34][35][36][37], unexpected rheological properties [38] and non-trivial behavior under shear [39][40][41][42][43].…”

Numerical Simulation of the Flows of Phototactic Microalgae Suspensions in an Illuminated Circular Channel

“…The forth-order accurate finite difference approximation was applied to the discretization of space, and the Crank-Nicolson method was applied to the time integration of Eqns. (12) and (21). Equation (23) …”